Near-field radiative heat transfer for structured surfaces

We apply an analytical approach for determining the near-field radiative heat transfer between a metallic nanosphere and a planar semi-infinite medium with some given surface structure. This approach is based on a perturbative expansion, and evaluated to first order in the surface profile. With the help of numerical results obtained for some simple model geometries we discuss typical signatures that should be obtainable with a near-field scanning thermal microscope operated in either constant-height or constant-distance mode.

Figure 1

Sketch of a probe-sample configuration with a square pad on a flat surface.

Figure 2

Sketch of an example structure, showing a particular value of the surface profile $hf\left(x,y\right)$ at $x=x_0$ and $y=0$.

Figure 3

Electric LDOS from Eq. (39) above a square pad with an edge length of 15 nm and a height of $h=5\text{nm}$ for two different observation distances [(a) $a=40\text{nm}$ and (b) $a=5.5\text{nm}]$ from the base plane. The frequency considered is $\omega ={10}^{14}{\text{s}}^{-1}$.

Figure 4

Plot of $hf\left(x,y\right)$ with the profile function defined by Eq. (45) with $d={10}^9{\text{m}}^{-1}$, $w=30\text{nm}$, and $h=5\text{nm}$.

Figure 5

LDOS of a gold half space structured by a gold bar (see Fig. 4). The frequency used is $\omega ={10}^{14}{\text{s}}^{-1}$ and the observation distance 10 nm. Observe the different scales for the electric LDOS (a) and the magnetic LDOS (b).

Figure 6

Dependence of the ratio of the first and zeroth order of the LDOS on the observation distance $a$ calculated above the profile shown in Fig. 4 for $x=0$ and frequency $\omega ={10}^{14}{\text{s}}^{-1}$.

Figure 7

Electric local density of states ($D_0^E$: dash-dotted line; $D_1^E$: dashed line; $D_0^E+D_1^E$: solid line) above the structured surface as depicted in Fig. 4 at a frequency of $\omega ={10}^{14}{\text{s}}^{-1}$ and a constant separation of 10 nm between observation point and surface.

Figure 8

Near-field radiative heat transfer between the structured sample depicted in Fig. 4 $\left(T_S=100\text{K}\right)$ and a spherical probe $\left(T_P=300\text{K}\right)$ with a radius of 10 nm in each case [(a) constant-height mode and (b) constant-distance mode].